I have Blender 2.8 installed on both of my computers, and I've tried every simple spin tool tutorial on Youtube, but only get the default blue Z (+)-(+) handle. Everywhere I've looked there is this selection window in the top left to select the desired axis and I've tried a number of different guesses / approaches -nothing. If anyone can help, thanks in advance! PS: I'm new, and not aware of how to post pics / video of my problem. Ken.
I suspect that the tutorial you saw was created on a beta version of 2.80 before around March this year. Later betas and the release version (2.80.75) moved those settings to the right-hand properties sidebar. Press the N key then the vertical 'Tools' tab on the edge of the window to show the settings indicated in the image below.